We had one national philanthropy and one local when I was in college.

APO is not housed under Fraternity and Sorority Life at Ole Miss (nor was it at Clemson). It's just another registered student organization that happens to have Greek letters. I presume Gamma Sigma Sigma or any other co-ed service group would be treated the same way there.

I'll also add that at Clemson Gamma Sigma Sigma was comprised entirely of female-identifying students even though they have no single-gender Title IX exemption. I don't know if they accomplished this exclusively through marketing themselves as an organization for women or through some other means, but some groups look different in practice than on paper.

Really depends on the school. A few have tried pulling all of the groups that actually pledge (regardless of what they call it) under the same umbrella as the NIC/NPC/NPHC GLOs. However, I'd expect that GSS like APO however is outside of "Official Greek Life" at the majority of its schools.

I don't have a good feeling for what degree Gamma Sigma Sigma's nationally created recruitment literature emphasizes that men can be in a chapter. The national website is pretty open about it (as opposed to Omega Phi Alpha which someone would assume based on everything national publishes online that they had a Title IX exemption)

Epsilon Sigma Alpha is another such organization. Nationally, they are supposed to be a co-ed service organization. But at Penn State, for example, they operate as an underground social sorority and only recruit women. The group was chartered by former Chi Omega members when they lost their recognition with their nationals.

These types of service organizations are not really part of the Greek system but would allow the OP to continue their service mission and maintain an organizational structure for her current sisters.